Your class, combined with a chosen Nature, determine how likely or unlikely you are to gain any stat points upon level ups. Untouched, each stat has a 45% chance of going up by 1 point with each level. Your chosen Nature will increase and decrease the chance of their respective stats (which are listed below, should you need it).
Leveling Up is determined by your performance in battle, as noted in the Battle Phase. Determined based on the strength of your opponent and the number of actions you performed. Each time you level, your character will have a chance of gaining a stat point in each of their stats based on their current % chance.
Each time you level up, you will also gain 1% that you may apply to any of your stats, bringing up the chance slightly of that stat leveling up later.